Skip to main content

Stochastic Inventory Models

  • Chapter
  • First Online:
The Logic of Logistics

Abstract

The inventory models considered so far are all deterministic in nature; demand is assumed to be known and either constant over the infinite horizon or varying over a finite horizon. In many logistics systems, however, such assumptions are not appropriate. Typically, demand is a random variable whose distribution may be known.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Archibald, B., & Silver, E. A. (1978). (s, S) policies under continuous review and discrete compound Poisson demand. Management Science, 24, 899–908.

    Google Scholar 

  • Arrow, K., Harris, T., & Marschak, J. (1951). Optimal inventory policy. Econometrica, 19, 250–272.

    Article  MathSciNet  MATH  Google Scholar 

  • Bell, C. (1970). Improved algorithms for inventory and replacement stock problems. SIAM Journal on Applied Mathematics, 18, 558–566.

    Article  MathSciNet  MATH  Google Scholar 

  • Chen, Y. F. (1996). On the optimality of (s, S) policies for quasiconvex loss functions. Working Paper, Northwestern University.

    Google Scholar 

  • Chen, F., & Zheng, Y. S. (1994). Lower bounds for multi-echelon stochastic inventory systems. Management Science, 40, 1426–1443.

    Article  MATH  Google Scholar 

  • Clark, A. J., & Scarf, H. E. (1960). Optimal policies for a multi-echelon inventory problem. Management Science, 6, 475–490.

    Article  Google Scholar 

  • Denardo, E. V. (1996). Dynamic programming. In Avriel, M., Golany, B. (Eds.), Mathematical programming for industrial engineers (pp. 307–384). Englewood Cliffs, NJ: Marcel Dekker.

    Google Scholar 

  • Eppen, G., & Schrage, L. (1981). Centralized ordering policies in a multiwarehouse system with lead times and random demand. In L. Schwarz (Ed.) Multi-level production/inventory control systems: theory and practice. Amsterdam: North-Holland.

    Google Scholar 

  • Federgruen, A., & Zipkin, P. (1984a). Approximation of dynamic, multi-location production and inventory problems. Management Science, 30, 69–84.

    Article  MATH  Google Scholar 

  • Iglehart, D. (1963a). Optimality of (s, S) policies in the infinite horizon dynamic inventory problem. Management Science, 9, 259–267.

    Google Scholar 

  • Iglehart, D. (1963b). Dynamic programming and stationary analysis in inventory problems. In H. Scarf, D. Guilford, M. Shelly (Eds.) Multi-stage inventory models and techniques (pp. 1–31). Stanford, CA: Stanford University Press.

    Google Scholar 

  • Lee, H. L., & Nahmias, S. (1993). Single product, single location models. In S. C. Graves, A. H. G. Rinnooy Kan, P. H. Zipkin (Eds.) Handbooks in operations research and management science, the Volume on Logistics of production and inventory (pp. 3–55). Amsterdam: North-Holland.

    Google Scholar 

  • Pang, Z. (2011). Optimal dynamic pricing and inventory control with stock deterioration and partial backordering. Operation Research Letter, 39, 375–379.

    Article  MATH  Google Scholar 

  • Porteus, E. L. (1990). Stochastic inventory theory. In D. P. Heyman, M. J. Sobel (Eds.) Handbooks in operations research and management science, the volume on Stochastic models (pp. 605–652). Amsterdam: North-Holland.

    Google Scholar 

  • Ross, Sheldon M. (1983). Introduction to Stochastic Dynamic Programming. Academic Press, INC., London.

    MATH  Google Scholar 

  • Ross, S. (1970). Applied Probability models with optimization applications. San Francisco: Holden-Day.

    MATH  Google Scholar 

  • Rosling, K. (1989). Optimal inventory policies for assembly systems under random demand. Operation Research, 37, 565–579.

    Article  MathSciNet  MATH  Google Scholar 

  • Scarf, H. E. (1960). The optimalities of (s, S) policies in the dynamic inventory problem. In K. Arrow, S. Karlin, P. Suppes (Eds.) Mathematical methods in the social sciences (pp. 196–202). Stanford, CA: Stanford University Press.

    Google Scholar 

  • Veinott, A. (1966). On the optimality of (s, S) inventory policies: new condition and a new proof. Journal SIAM Applied Mathematics, 14, 1067–1083.

    Google Scholar 

  • Veinott, A., & Wagner, H. (1965). Computing optimal (s, S) inventory policies. Management Science, 11, 525–552.

    Google Scholar 

  • Zheng, Y. S. (1991). A simple proof for the optimality of (s, S) policies for infinite horizon inventory problems. Journal of Applied Probability, 28, 802–810.

    Google Scholar 

  • Zheng, Y. S., & Federgruen, A. (1991). Finding optimal (s, S) policies is about as simple as evaluating a single policy. Operation Research, 39, 654–665.

    Google Scholar 

  • Zipkin, P. H. (2000). Foundations of inventory management. Burr Ridge, IL: Irwin.

    Google Scholar 

  • Zipkin, P. H. (2008). On the structure of lost-sales inventory models. Operation Research, 56, 937–944.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

Simchi-Levi, D., Chen, X., Bramel, J. (2014). Stochastic Inventory Models. In: The Logic of Logistics. Springer Series in Operations Research and Financial Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9149-1_9

Download citation

Publish with us

Policies and ethics